Welcome to the forum!
Hhmm, EXR, let's see.... Would that be OpenEXR (
https://en.wikipedia.org/wiki/OpenEXR) ?
As a raster format, and as far as I know (since this is the first I've heard of it) you can import it into Inkscape. But for editing, you'd be very limited. You'd be better off using a raster graphics editor for that. And when it's finished being edited, then import it into Inkscape as your background.
Do you already understand the difference between raster and vector graphics?
Edit
For editing a raster image, you'd be limited to some broad color adjustments (Extensions menu > Raster) and clipping or maybe masking.